A Numerical Approach to Solve Oscillatory Epidemiological Models

Abstract This study presents the development and application of a new implicit block method for solving first-order oscillatory differential equations with a particular focus on epidemiological models. The proposed numerical method is constructed using power series polynomials through interpolation and collocation techniques to achieve higher accuracy and improved computational efficiency. The method is analyzed in terms of its basic properties, including order, error constant, consistency, zero-stability, convergence, and region of absolute stability. Numerical experiments are conducted on three practical models: the SIR (Susceptible-Infective-Recovered) model, a mixture model relevant to chemical processing, and a radioactive decay model. Comparative error analysis demonstrates that the new method outperforms existing approaches in terms of accuracy and computational stability. The results affirm the suitability of the developed block method for simulating stiff and oscillatory systems, making it a valuable tool in applied numerical analysis, particularly within epidemiology and related scientific fields.